Usually this is what i do in half guard in gi to get back. Im just a new blue so take it as you will. But i think the half guard was what got me my blue at 1 year mark. The rest of my game aint so great at the moment.

In half-guard I get the underhook which is the easiest part. I control the opposing arm with my free arm so i dont get my arm broken in the following step, I strecht the other arm away from my opponent and circle inside for the underhook.

Or get the distance with quarter then go back in like your photos.

Now that i think about it, i used to arm drag from half guard so i could jump on their back. Most instances they pull back, in which case you follow them to slide in the underhook. Theres also a couple of choke from the arm drag. But i like to focus on getting the back.

I grab his opposing lapel because it gives me better leverage ( so yeah i undress him a bit). That also because Ill be pulling alot, so his gi will be undone and I have a feed later on. If he gets rid of the underhook, you get the choke because of the feed.

Anyways that being said, if he pulls back, I follow straight on to sweep him.
If following straight on doesnt work, somewhat stand up with a hook still in to circle around him, jump on back.

Thinking about it, if they kept the posture, I use a combination of armdragging and circling to his back. Do it alot, he opens up eventually.

If I get crushed on by his weight. I Push on his opposing knee so that he drops his weight away from you, also helping me scoot. Swing one leg over his back. Im lanky enough to grab my ankle so i can make it slide in to get both hooks. But if i need to scoot more, i grab my ankle and kick which will scoot my butt.

If he tries to clock choke your or something, disengage into quarter then go back in.

If he stands up, I feed his gi and try to take him down, but mostly i feed the bottom of his gi and swing inside. On most time he will sit you on. It sucks to have a butt on your cheek, but eventually he tires, and I reversed position. Basically the same technique as the last video of your post .

And if he fully stands, single leg or delariva.

And if things really go out of hand and hes about to slip out , x guard from under or incidentally the same technique which youve posted the photos with the kanji.

The only thing killed me in half guard was an experienced heavier and stronger judoka planting his fist in my throat and pinning it to the floor. That sucked.

Nowadays I hardly play any other half guard game but alternating backdoor and quarter guards.

Why? What could have inspired me to forget about the traditional on your side with underhooks game? Are we going to have to have a very serious talk about your basics, young man?

Well, I do these because they play on your opponent's sense of triumph. Objectively, being in quarter guard with the guy hugging your thigh feels like you're getting mount. His kinesthetic sense thinks he's advancing when he's not.

More on that later, but objectively speaking, the deep and quarter (hereafter referred to as the "ranma 1/4") are great places to be. You're way under his center of gravity and most people have no idea how to counter.

However, if reading Eddie Bravo's books has taught me anything it's that getting to these good sub-positions often requires going through a set of small, incremental improvements: Breaking posture, opening the arms, getting a hand to the mat, etc. Also it's important to constantly, smirkingly talk about your love of herb and look like a greasy Las Vegas jigolo.

So the first step is getting there. How?

-Whip up
-Jaws of life to a hip push
-front naked choke counter
The front naked choke is the perfect opportunity to go for this. Push his elbows forward (in the direction of your head) as you shoot your hips down and in the direction of the trapped leg. Quickly relock quarter guard around his shin and hug that thigh for all it's worth. It takes some balls to ignore an in progress choke, but do it anyway.
-knee through pass counter
Use this when he brings his knee up and between your legs while you're playing open guard. Close quarter guard around his calf and hug. As he passes, you can roll belly down and Old School.

You can even pull this from standing from a failed tani otoshi or something.

Ok, now you're down here. What's this game like? Well the first thing to remember is not to let go of that leg. If you hug it, you can still recover even if he's practically advanced to moutn.

Let's assume you're playing quarter guard on his left leg. Your next step is going to be determined by where his knee rests.

If his knee is on your right:
This is gravy. Belly down and single leg sweep every time. On those rare occasions you dont' get it (almost always when you accidentally lose the foot as you go belly down), you can easy transition to the Dogfight.

If his knee is centered:
Crap, he's got good weight control. Put lockdown on and roll backwards over your right shoulder, not letting go of the leg.

If his knee is on your left.
Uh oh. Feels like mount. Well, it could be, but it's not guaranteed if you think on your feet. Now you can unhug. Push the thigh of the formerly hugged leg with both arms so his legs splay. Bring your bottom knee inside this new space. Now you can do the pickup single/tactical standup sweep.
Alternatively, your unused leg (the former top leg) can be thrown over his right back thigh, basically omoplataing on his non-captured leg, which lets you put on a surprise toe-hold

Why not the traditional deep game?
Here's my take on this, and I learned this from bitter experience. The deep game is just not worth it. Why?

Because the counter's too simple.

Consider:

Bottom man's already starting to get crossfaced in this picture. With the shoulder crossface comes him splaying his legs out and sprawling down hard. Now you've lost the leg to his crossface and sprawl and he's probably working for an underhook on the right side if you go by the picture as reference. You can't take advantage of his legs splaying because the crossface flattened you and moved your upper body out of position, and it feels like you're losing the trapped leg.

I am very tired. More tommorow.

"The only important elements in any society
are the artistic and the criminal,
because they alone, by questioning the society's values,
can force it to change."-Samuel R. Delany

RENDERING GELATINOUS WINDMILL OF DICKS

THIS IS GOING TO BE THE BEST NON-EUCLIDIAN SPLATTERJOUST EVER

It seems that the only people who support anarchy are faggots, who want their pathetic immoral lifestyle accepted by the mainstream society. It wont be so they try to create their own.-Oldman34, friend to all children

I guy I train under (Matt Thornton purple belt) has taught me (and I have been using this) to use my forearm to block the cross face. Think of the T-Rex position that Eddie Bravo uses in his book (or think of how Muay Thai fighters hold their arms out when fighting). As soon as they are about to crossface you then use the T-Rex (as I've started calling it as it helps me remember it). Also, plant your forehead into the back of your hand for extra power and stability for the move. By doing this, you use create enough space to shrimp to your side which makes it harder to get crushed. T-Rexing your opponents crossface arm is also a good way to get your underhooks faster and with less of a fight. If you opponent is applying a large amount of pressure into getting the cross face then this allows you to transition into the half butterfly guard like you normally play and sweep. They are so intent on the crossface that you can use your T-Rex to trap and sweep at the same time. They won't expect it.

Aesopian,
Here's some things I tell guys who want to work half-guard, although I'm not sure if they
1) Stay on your side - so on my right side my right arm is blocking his left bicep to stop the cross-face.
2) Don't go for the underhook too early.
3) Keep your opponent's weight on his hands. If his weight's on his hands he can't choke you or put weight on you. Do this by grabbing his belt and pulling him forward constantly.
4) When you do underhook then underhook the leg, not the back.

You probably know all this stuff already, but I find that ensuring I stay on my side and pulling the guy forwards means I have less trouble.